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4 votes
Given the side lengths of 2, 2, and 3, the triangle is:

acute.
obtuse.
right.
None of these choices are correct.

1 Answer

4 votes

Answer: Obtuse

Step-by-step explanation:

The converse of the pythagorean theorem has 3 cases

  • If
    a^2+b^2 > c^2 then the triangle is acute.
  • If
    a^2+b^2 = c^2 then we have a right triangle.
  • If
    a^2+b^2 < c^2 then the triangle is obtuse.

a = 2, b = 2, c = 3 are the three sides. C is always the largest side.


a^2+b^2 = 2^2+2^2 = 8


c^2 = 3^2 = 9

We can see that
a^2+b^2 < c^2 (since 8 < 9), which leads to the triangle being obtuse. The obtuse angle is opposite the longest side.

You can use a tool like GeoGebra to confirm the answer.

User TWGerard
by
7.9k points

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